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MiS Preprint
63/2011

Robustness and Conditional Independence Ideals

Johannes Rauh and Nihat Ay

Abstract

We study notions of robustness of Markov kernels and probability distribution of a system that is described by $n$ input random variables and one output random variable. Markov kernels can be expanded in a series of potentials that allow to describe the system's behaviour after knockouts. Robustness imposes structural constraints on these potentials.

Robustness of probability distributions is defined via conditional independence statements. These statements can be studied algebraically. The corresponding conditional independence ideals are related to binary edge ideals. The set of robust probability distributions lies on an algebraic variety. We compute a Gröbner basis of this ideal and study the irreducible decomposition of the variety. These algebraic results allow to parametrize the set of all robust probability distributions.

Received:
Sep 29, 2011
Published:
Sep 29, 2011
MSC Codes:
13P25, 13P10, 62H20

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Preprint
2011 Repository Open Access
Johannes Rauh and Nihat Ay

Robustness and conditional independence ideals